Tree Diagrams and Fundamental Counting Principle

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all the possible outcomes of a sequence of events, branching out from a starting point.

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in m x n ways.

Front

How many different license plates can be made with 2 letters followed by 1 digit?

Back

6760, calculated as 26 (letters) x 26 (letters) x 10 (digits) = 6760.

Front

If you have 5 shirts, 3 jackets, 2 pants, and 3 shoes, how many outfits can you create?

Back

90, calculated as 5 (shirts) x 3 (jackets) x 2 (pants) x 3 (shoes) = 90.

Front

How many different pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

192, calculated as 8 (meats) x 4 (cheeses) x 3 (crusts) x 2 (sauces) = 192.

Front

How many different 4-digit codes can be created using numbers 0-9 without repetition?

Back

5,040, calculated as 10 (choices for the first digit) x 9 (for the second) x 8 (for the third) x 7 (for the fourth) = 5,040.

Front

What is the total number of outcomes if you have 3 different types of hats and 4 different shirts?

Back

12, calculated as 3 (hats) x 4 (shirts) = 12.

Front

If you can choose 2 toppings from 5 available toppings, how many combinations can you make?

Back

10, calculated using combinations: 5 choose 2 = 5! / (2!(5-2)!) = 10.

Front

What is the formula for calculating permutations of 'n' items taken 'r' at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.